pancakeSort :: Ord a => [a] -> [a]
pancakeSort [] = []
pancakeSort cakeStack =
    let selectedCake = indexOfLargest cakeStack
        cakeStack' = (doFlip (length cakeStack)) . (doFlip selectedCake) $ cakeStack
    in (pancakeSort (init cakeStack')) ++ [last cakeStack']



indexOfLargest :: Ord a => [a] -> Int
indexOfLargest (x:xs) =
    let f m i j y = if length y == 0
                        then i
                        else if (head y) > m
                                then f (head y) j (j+1) (tail y)
                                else f m i (j+1) (tail y)
    in f x 0 1 xs



doFlip :: Int -> [a] -> [a]
doFlip depth list =
    let prefix = take (depth + 1) list
        rest = drop (depth + 1) list
    in (reverse prefix) ++ rest